Experimental detection of Hopf bifurcation in two-dimensional dynamical systems

Jiménez-Ramírez, Omar; Cruz–Domínguez, E.J.; Quiroz-Juárez, Mario A.; Aragón, J. L.; Vázquez-Medina, Rubén

doi:10.1016/j.csfx.2021.100058

Cited by 7 publications

(3 citation statements)

References 12 publications

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“…In this device, the physical quantities from the problem to be solved such as fluid, pressure, or velocity, are represented by voltage signals, so the temporal evolution of the variables of interest is directly measured on the analog circuit. This has enabled the implementation of experimental systems that offer certain advantages over the original physical systems [13][14][15][16][17] . Especially, analog computers are suited to simulate dynamical systems [18][19][20][21][22][23] , and even, stochastic dynamical systems 24,25 .…”

Section: Chaotic and Periodic Regimesmentioning

confidence: 99%

Classical harmonic three-body system: an experimental electronic realization

Escobar-Ruiz

Quiroz-Juárez

Río-Correa

et al. 2022

Sci Rep

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The classical three-body harmonic system in $${\mathbb {R}}^d$$ R d ($$d>1$$ d > 1 ) with finite rest lengths and zero total angular momentum $$L=0$$ L = 0 is considered. This model describes the dynamics of the $$L=0$$ L = 0 near-equilibrium configurations of three point masses $$(m_1,m_2,m_3)$$ ( m 1 , m 2 , m 3 ) with arbitrary pairwise potential $$V(r_{ij})$$ V ( r ij ) that solely depends on the relative distances between bodies. It exhibits an interesting mixed regular and chaotic dynamics as a function of the energy and the system parameters. The corresponding harmonic quantum system plays a fundamental role in atomic and molecular physics. In this work we report on a novel electronic experimental realization of the model as a complementary tool to analyze the rich dynamics of the classical system. Our setup allows us to experimentally explore different regions of behavior due to the fact that the intrinsic parameters and initial states of the system are independently set by voltage inputs. Chaotic and periodic motions are characterized employing time series, phase planes, and the largest Lyapunov exponents as a function of the energy and system parameters. The results show an excellent qualitative as well as quantitative agreement between theory and experiment.

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Section: Chaotic and Periodic Regimesmentioning

confidence: 99%

Classical harmonic three-body system: an experimental electronic realization

Escobar-Ruiz

Quiroz-Juárez

Río-Correa

et al. 2022

Sci Rep

View full text Add to dashboard Cite

show abstract

“…In general, a reparameterization to a single, unambiguous bifurcation parameter may be possible in principle, but often requires either substantial additional physical insight, or mathematical sophistication, or both. Some researchers have even recommended building an analogous physical circuit as the fastest method to detect the bifurcation [25]. Complex models can have hundreds of coupled dynamical equations with thousands of parameters (e.g., models of sophisticated mobile phone circuit boards [26], or complex protein networks [27]).…”

Section: A Bifurcationsmentioning

confidence: 99%

Sloppy model analysis identifies bifurcation parameters without Normal Form analysis

Anderson¹,

Transtrum²

2022

Preprint

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Bifurcation phenomena are common in multi-dimensional multi-parameter dynamical systems. Normal form theory suggests that the bifurcations themselves are driven by relatively few parameters; however, these are often nonlinear combinations of the bare parameters in which the equations are expressed. Discovering reparameterizations to transform such complex original equations into normal-form is often very difficult, and the reparameterization may not even exist in a closed-form.Recent advancements have tied both information geometry and bifurcations to the Renormalization Group. Here, we show that sloppy model analysis (a method of information geometry) can be used directly on bifurcations of increasing time scales to rapidly characterize the system's topological inhomogeneities, whether the system is in normal form or not. We anticipate that this novel analytical method, which we call time-widening information geometry (TWIG), will be useful in applied network analysis.

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“…Kumar and dipesh also examined the allelochemical effect on competing plant populations [7][8][9]. Medina et al detect the hopfbifurcation in two parameter space [10]. Kumaran et al examined the rate of evolution of the probabilistic density function of a state variables controlled by the stochastic delay differential equation (SDDE) with combined white noise as well as coloured disturbances change [11].…”

Section: Introductionmentioning

confidence: 99%

A novel approaches to 6th-order delay differential equations in toxic plant interactions and soil impact: beyond newton-raphson

Dipesh,

Kumar

2024

Phys. Scr.

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This paper focuses on investigating a 6th-order delay differential equation root within the context of toxic interactions between competing plant populations and their impact on soil dynamics. The study introduces a novel approach for approximating solutions to nonlinear delay differential equations, drawing inspiration from the fundamental principles of Newton-Raphson's method. This technique leverages the complex root theorem to ensure stability, enabling it to effectively handle widely dispersed roots within dynamic systems. Consequently, this approach holds considerable potential for a diverse array of applications. The analysis introduces time delay into a nonlinear dynamical system and explores the system's threshold value. At this threshold, the dynamical system's stability undergoes fluctuations, and observations of Hopf bifurcation phenomena are made. The study also successfully identifies both real and complex roots of the dynamical system. Visualization of the dynamic system is accomplished using MATLAB-generated graphical representations. Moreover, this research's implications extend to the realm of climate action and terrestrial ecosystems, underscoring its significance for promoting a sustainable environment and fostering healthy life on land.

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Experimental detection of Hopf bifurcation in two-dimensional dynamical systems

Cited by 7 publications

References 12 publications

Classical harmonic three-body system: an experimental electronic realization

Classical harmonic three-body system: an experimental electronic realization

Sloppy model analysis identifies bifurcation parameters without Normal Form analysis

A novel approaches to 6th-order delay differential equations in toxic plant interactions and soil impact: beyond newton-raphson

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